Discrete Applied Mathematics Seminar by Josh Hallam: Parking Functions and Noncrossing Partitions of Graphs

Speaker: Josh Hallam, Loyola Marymount

Title: Parking Functions and Noncrossing Partitions of Graphs

Abstract:  Imagine you have a row of parking spots labeled 1 through n on a one-way street.  Moreover, suppose you have n cars lined up to park and that each car has a preferred parking spot.  The cars come in, one by one, driving to their preferred spot. If it is open, they park there, otherwise they continue to the next available spot if there is one.  We say the sequences of preferred spots is a parking function if each car is able to park.  Parking functions were originally studied from a computer science perspective, but over time have been shown to have many applications in mathematics.  Stanley showed a beautiful connection between parking functions and noncrossing partitions via the noncrossing partition lattice.  Farmer, Hallam, and Smyth introduced and studied a generalization of the noncrossing partition lattice to graphs.  Later, in joint work with Anna Salam, we characterized which graphs retain this nice connection with parking functions.

No background in parking functions or noncrossing partitions will be assumed.

 

Discrete Applied Math Seminar

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